Lavista enrolled the Composition Workshop (Taller de Composición) at the National Conservatory in 1963, under the guidance of Carlos Chávez, Héctor Quintanar, and Rodolfo Halffter. In 1967 he received a scholarship from the French government to study at the Schola Cantorum in Paris, where he studied with Jean Etienne Marie. During his time in Europe, he attended courses by Henri Pousseur, Nadia Boulanger, Christoph Caskel, and Karlheinz Stockhausen.In 1970 he founded Quanta, a collective improvisation group. He also worked at the electronic music studio of radio ant television in Tokyo in 1972. At the end of the 1970s and beginning of the 1980s he closely collaborated with renowned performers in solo and chamber works where he explored unusual timbre possibilities by the use of extended techniques. In 1982, he founded Pauta, one of the most important music journals in Latin America, and continues to serve as its chief editor. In 1987, he received a Guggenheim Fellowship for his first (and only) opera Aura, based on the short story by Carlos Fuentes. Aura premiered in 1988 at the Palacio de Bellas Artes in Mexico City
Lavista has approached religious genres in a series of compositions where he uses Medieval and Renaissance procedures, such as the symbolic use of certain intervals, canonic permutations, and isorhythm, most evident in the Missa ad Consolationis Dominam Nostram, a central work in his oeuvre.He has received multiple awards and honors: Premio Nacional de Ciencias y Artes and the Medalla Mozart in 1991, an honorable mention from the Sistema Nacional de Creadores del Fondo Nacional para la Cultura y las Artes in 1993, and membership in the prestigious El Colegio Nacional since 1998. Lavista’s works are frequently performed in Europe and throughout the Americas, where he travels regularly to give lectures and seminars in composition. Since 1970 he teaches music analysis and composition at the National Conservatory in Mexico City. Additionally, he has been visiting professor at the University of Chicago, Cornell University, the University of California San Diego, Indiana University, McGill University and University of North Texas.
He has also composed incidental music for plays, film scores (mostly in conjunction with Nicolás Echevarría), orchestral pieces, and vocal music.